April claims that 1 + cos?(0)_ 1 sin (0) sin (0) is an identity for all real numbers 0 that follows from the Pythagorean identity a. For which values of 0 are the two functions f(0) = 1+ cos@ and g(0) = 1 sin (0) - defined? sin (0) seabby wind now b. Show that the equation 1 + Cos (@) 1 sin (0) sin (0) - follows from the Pythagorean identity. C. Is April correct? Explain why or why not. Write the equation 1 + cost(0) 1 d. -in terms of other trigonometric functions, and state the resulting sin (0) sin (0) identity. erbfod no enolfort 203 Prove the identity and restrict the domain if needed. csc2 0 = 1 + cot2 0 Recall the Pythagorean identity sin2(0) + cos?(0) = 1, where 0 is any real number. a. Find sin(x), given cos(x) = , for -"